[Statics - Torques] Determining Coefficient of Static Friction

[erickbq]

Homework Statement

The top of a ladder of L and mass m is connected to a wall by a horizontal cable. The ladder makes an angle Θ=60 with the horizontal. A woman of mass 2m finds that as she climbs the ladder, the ladder begins to slip when she is one-third of the way up the ladder.

Find the coefficient of static friction between the ladder and the ground.

Homework Equations

(F⃗ net)x=ΣFx=0

(F⃗ net)y=ΣFy=0

Στ=0

τ = (radial distance)(F)

The Attempt at a Solution

a) Determined all relevant forces associated with ladder.
b) Plotted each force onto a free-body diagram.
c) Created a table with forces and their respective components
c-1) Determined torque by finding the radial distance from center of rotation (c.o.r.) to force.
d) Solved for μs.

My answer turns out to be incorrect. The answer to this question is 0.225 while I get 0.333... .

 

[haruspex]

The diagram is fine, but there seem to be some errors in your torque equation. Check that you have the sense of each torque correct and that you are using sin and cos appropriately.